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Anni [7]
3 years ago
7

Jamie lost 27 pounds in one year. on average how many pounds did jamie lose per month?

Mathematics
2 answers:
never [62]3 years ago
8 0

2.25 pounds because you divide 27 divided by 12. Which the 12 is months. Hope this helps. :^)


aleksandr82 [10.1K]3 years ago
3 0
Since there are 12 months in a year, all we need to do is divide 27 pounds by 12, and we get that he lost, on average, 2.35lbs per month.
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Sliva [168]

Answer:

\displaystyle - \frac{1}{2}

Step-by-step explanation:

we would like to compute the following limit:

\displaystyle  \lim _{x \to 0} \left( \frac{1}{  \ln(x +  \sqrt{  {x}^{2}  + 1} ) } -  \frac{1}{  \ln(x + 1) }  \right)

if we substitute 0 directly we would end up with:

\displaystyle\frac{1}{0}  -  \frac{1}{0}

which is an indeterminate form! therefore we need an alternate way to compute the limit to do so simplify the expression and that yields:

\displaystyle  \lim _{x \to 0} \left( \frac{ \ln(x + 1) -  \ln(x +  \sqrt{ {x}^{2} + 1 } }{  \ln(x +  \sqrt{  {x}^{2}  + 1} )  \ln(x + 1)  }  \right)

now notice that after simplifying we ended up with a<em> </em><em>rational</em><em> </em>expression in that case to compute the limit we can consider using L'hopital rule which states that

\rm \displaystyle  \lim _{x \to c} \left( \frac{f(x)}{g(x)}  \right)  = \lim _{x \to c} \left( \frac{f'(x)}{g'(x)}  \right)

thus apply L'hopital rule which yields:

\displaystyle  \lim _{x \to 0} \left( \frac{  \dfrac{d}{dx}  \ln(x + 1) -  \ln(x +  \sqrt{ {x}^{2} + 1 }  }{   \dfrac{d}{dx} \ln(x +  \sqrt{  {x}^{2}  + 1} )  \ln(x + 1)  }  \right)

use difference and Product derivation rule to differentiate the numerator and the denominator respectively which yields:

\displaystyle  \lim _{x \to 0} \left( \frac{ \frac{1}{x + 1}  -  \frac{1}{ \sqrt{x + 1} }  }{ \frac{ \ln(x + 1)}{ \sqrt{ {x}^{2}  + 1 }     }    +  \frac{  \ln(x +  \sqrt{x ^{2} + 1 }  }{x + 1} }  \right)

simplify which yields:

\displaystyle  \lim _{x \to 0} \left( \frac{ \sqrt{ {x}^{2} + 1  } - x - 1 }{  (x + 1)\ln(x  + 1 )  +  \sqrt{ {x}^{2}  + 1} \ln( x + \sqrt{ {x }^{2}  + 1} )   }  \right)

unfortunately! it's still an indeterminate form if we substitute 0 for x therefore apply L'hopital rule once again which yields:

\displaystyle  \lim _{x \to 0} \left( \frac{  \dfrac{d}{dx} \sqrt{ {x}^{2} + 1  } - x - 1 }{  \dfrac{d}{dx}  (x + 1)\ln(x  + 1 )  +  \sqrt{ {x}^{2}  + 1} \ln( x + \sqrt{ {x }^{2}  + 1}  )  }  \right)

use difference and sum derivation rule to differentiate the numerator and the denominator respectively and that is yields:

\displaystyle  \lim _{x \to 0} \left( \frac{  \frac{x}{ \sqrt{ {x}^{2} + 1 }  }  - 1}{      \ln(x + 1)   + 2 +  \frac{x \ln(x +  \sqrt{ {x}^{2} + 1 } ) }{ \sqrt{ {x}^{2} + 1 } } }  \right)

thank god! now it's not an indeterminate form if we substitute 0 for x thus do so which yields:

\displaystyle   \frac{  \frac{0}{ \sqrt{ {0}^{2} + 1 }  }  - 1}{      \ln(0 + 1)   + 2 +  \frac{0 \ln(0 +  \sqrt{ {0}^{2} + 1 } ) }{ \sqrt{ {0}^{2} + 1 } } }

simplify which yields:

\displaystyle - \frac{1}{2}

finally, we are done!

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